verification of the quasi-steady approximation for sound ... · approximation for sound generation...

The 3rd Biennial ICVPB MeetingSept. 13-16 2002, Denver, Colorado

Verification of the quasi-steady approximation for sound generation by

confined pulsating jets

L. Mongeau, Z. Zhang, S. Thompson, and S.H. FrankelSchool of Mechanical Engineering

Purdue University


For more information:

see web site at:http://widget.ecn.purdue.edu/%7Evoice/

http://widget.ecn.purdue.edu/%7Evoice/


AcknowledgementsSponsor

• subcontract, NIDCD (R01 DC03577)• Ronald C. Scherer, P.I., BGSU

Graduate Students• Zhaoyan Zhang (Postdoc, U. Maryland)• Scott Thomson (Ph.D., summer 2003)• Jong Beom Park

Collaborators• Steve H. Frankel, Assoc. Prof.

Technical Assistance• Gilbert Gordon


Objectives

Investigate the range of validity of the quasi-steady approximation• Periodic Component• Random, broadband component

Gain a better understanding of the sound generation mechanisms• periodic and broadband components• steady and pulsating confined jet flows


Intra-Glottal Flows

sub-glottal

supra-glottal

glottal

flow

Asub

Asup

Ag

turbulencejet

re-circulation

re-attachment


Bernouilli’s equation

2sub sup 0 c

1p p U2

− = ρ

assumptions:• irrotational• flow incompressibe• along a streamline• viscous effects neglected• acceleration effects neglected


Bernouilli’s Obstruction Theory

sub upg

0

2(p p )Q KA

−=

ρassumptions:• large area ratio Asub/Ag• flow coefficient K combines discharge

coefficient and approach velocity factor• K=K(shape, area, inflow+outflow condition)• same as Bernouilli’s equation• all variable instantaneous (except density)


Simplified Circuit

ps

Rg(t)

Lg=0

vocal tract

0 0L

tube

cRAρ

=LungPressure

assumptions:• infinitely long tube• receiver close to orifice• negligible inductive effects

glottal resistance

Q

psup (t)

x

Flow

z

y

Orifice with area Ag(t)

Tube with area At

x

Flow

z

y

Orifice with area Ag(t)

Tube with area At


Glottal Resistance

sub up sub upg

sub upg

0

p p p pR

Q 2(p p )KA

− −= =

−ρ

• K=K(Ag,psub- psup)

• direct measurement of Ag, psup, psub sufficient to

calculate Rg

• quasi-steady approximation states that for

given geometry, Ag and ∆p, Rg is the same for

steady or pulsating flows


Non-Stationary Phenomena• dφ/dt• Vorticity shedding• Large scale turbulent structures• Flow induced by motion of wall


Rubber Dynamic Physical Models

Advantages• real size (no need for scaling)• allow acoustic and simple flow

measurements• orifice shape easy to modify• easy to add complexity to model geometry

Disadvantages• real size (can’t easily perform detailed flow

measurements for validation of CFD)• some shape distortion at high frequency


Experimental FacilityInertial base (concrete slab)Two large electro-dynamic shakers+power amplifiersRectangular Acrylic test sections

• anechoic terminations• open tubes of different lengths

Flow supply and controller• air, helium, and CO2 mixtures

Rubber glottis models (real size)• molds machined using Stereo Lithography• geometry defined using CAD (proE)• three geometries (convergent, straight, and

divergent)Belt mechanical drive used for flow visualization


shaker #1

shaker #2

flow

orifice plate


100 Hz

70°

15° 15°

70° 70°

1.5 1.5 1.5

1.5

17.5

(a) (b) (c)

(d)

Dimensions in mm

70°

15° 15°

70° 70°

1.5 1.5 1.5

1.5

17.5

(a) (b) (c)

(d)

Dimensions in mm


Tube configurations

M(14) M(9) P(5)P(5) M(9) M(14)

Anechoic termination Anechoic termination

AA

M(14) M(9) P(5)P(5) M(9) M(14)

Anechoic termination

LL

M(14) M(2.5)

P(2.5)P(2.5)

M(2.5) M(14)

Anechoic termination

HW

AA

LL

HW


0 50 100 150 200 250 300 350 400 450 5000.0

0.2

0.4

0.6

0.8

1.0

Mag

nitu

de

Frequency (Hz)

Reflection coefficients

0 500 1000 1500 2000 2500 30000.0

0.2

0.4

0.6

0.8

1.0

Mag

nitu

de

Frequency (Hz)

Downstream

Upstream

AA

LL


InstrumentationTwo pairs of phased-matched microphonesPrecision manometerPrecision gas flow meterPhotoelectric detector and light sourceAccelerometersHot-wire anemometer (up to 6 channels)Data acquisition systemsSmoke generatorHigh-speed camera (NAC)


microphones

hot-wireprobe

pressure X-ducer

accelerometer

flow

shaker


Flow Visualization

1 cm

converging

diverging

span view width view

steady open jet, 4 cm H2O


Bernouilli’s EquationDirect verification

hot-wire anemometer


Hot-wire velocity data

Fraction of one cycle

f =100 Hz, ∆ p =12 cm H2O, conv, HW

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

0

10

20

30

40

50

60

HWBernoulli

Cen

terli

ne v

eloc

ity (m

/s)

closed

open

0 5 10 15 20 25 3010

20

30

40

50

60

70

Cen

terli

ne v

eloc

ity (m

/s)

Pressure drop across orifice (cm H2O)

static

0 5 10 15 20 25 3010203040506070 H.W.

Bernoulli's

Cen

terli

ne v

eloc

ity (m

/s)

Pressure drop across orifice (cm H2O)


Bernouilli’s Obstruction TheoryIndirect Method

• can’t easily measure instantaneous flow rate

• use inverse filter methodequivalent monopole strength


Assumptions• flow through orifice at any instant same

as steady incompressible flow for same wall geometry and inlet boundary condition

• monopole source• plane waves• source strength is fluctuating volume

velocity at orifice


Procedures• iteration method• Predict sound pressure using Bernouilli’s

equation (steady form), using measured orifice area, mean pressure drop across the orifice, and orifice discharge coefficients measured statically

• Reflections accounted for using signal processing techniques (deconvolution)• two-microphone method• low-pass filter


equivalent monopole source model

•Dipole source due to unsteady pressure drop

•similar to vibrating piston•Decompose into two monopole sources with equivalent source strength, each radiating to one side of the orifice

•two equivalent monopole sources equal in strength and opposite in phase

InletObserver

Piston

Upstream Downstream

Outlet

- +Upstream Downstream

Orifice

Acousticloading Rup

Acousticloading Rdw

Flow

Monopole sources


202

10 ),0('),0(')( cdnup Utptpptp ρ=−+∆=∆

cgd UACQ =

∫ −−=⋅−= +− })({1}{),0(

),0(' 0)()(

0QtQ

AdeRe

cB

tut

kLtjkLtjupup ω

ρω ωω

})({1}{),0(

),0(' 0)()(

0

QtQA

deRec

Btut

kLtjkLtjdndn −=⋅−= ∫ +− ω

ρω ωω

∫ ⋅+= −+−− ωω ωω deRexBtxp xLktjxLktj }ˆ){,(),(' ))(())((

Cd: orifice discharge coefficient obtained in steady flow measurementR: reflection factor measured using two-microphone methodB: coefficient to be determinedAt: orifice area measured using a photoelectric sensor


Typical ResultComparison between measured upstream sound pressure and

prediction from quasi-steady assumption

0 0.2 0.4 0.6 0.8 1-3

-2

-1

0

1

2


Soun

d pr

essu

re (c

m H

2O)

Measured Predicted

f=120Hz∆p=12 cm

H2O


Results•f=80 Hz, ∆p0=12 cm H2O, convergent orifice, AA

0 0.2 0.4 0.6 0.8 1-3

-2

-1

0

1

2

3


Mea

sure

d ac

oust

ic p

ress

ure

(cm

H2O

)

0 0.2 0.4 0.6 0.8 1-3

-2

-1

0

1

2

3


Mea

sure

d ac

oust

ic p

ress

ure

(cm

H2O

)

0 0.2 0.4 0.6 0.8 1 1.2-300

-250

-200

-150

-100

-50

0

50

100

150

200


Volu

me

velo

city

sou

rce

stre

ngth

(ml

0 0.2 0.4 0.6 0.8 1 1.2-300

-250

-200

-150

-100

-50

0

50

100

150

200


Volu

me

velo

city

sou

rce

stre

ngth

(ml

Volume Velocity source

Raw pressure

UpstreamDownstream * (-1)


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-4

-2

0

2

4

6


Non

- dim

ensi

onal

vol

ume

velo

city

so

urce

str

engt

h (m

l/s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-4

-2

0

2

4

6


Non

- dim

ensi

onal

vol

ume

velo

city

so

urce

str

engt

h (m

l/s)

Effects of Mean Pressure

Volume velocity source at different pressure drop scaled by the square root of the mean pressure drop. Straight orifice, f=120 Hz.

12 cmH2O

9 cmH2O

6 cmH2O


Effects of Driving Frequency

0 0.2 0.4 0.6 0.8 1

-200

-150

-100

-50

0

50

100

150

200

250

Fraction of one cycle0 0.2 0.4 0.6 0.8 1

-200

-150

-100

-50

0

50

100

150

200

250


-200

-150

-100

-50

0

50

100

150

200

250


-200

-150

-100

-50

0

50

100

150

200

250


Raw

Volume velocitysource strength (ml/s)

Convergent orifice∆p0=12 cm H2O

70 Hz100 Hz120 Hz

Deconvolved


•Driving frequency has small effect on source strength•consistent with quasi-steady assumption


Effects of acoustic loading

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

-1.0

-0.5

0.0

0.5

1.0

1.5

Aco

ustic

pre

ssur

e (c

m H

2O)


With FlowWithout Flow

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2-500

-400

-300

-200

-100

0

100

200

300

400

Volu

me

velo

city

sou

rce

(ml/s

)


DownstreamUpstream * (-1)

• downstream tube modeled as close-open tube

• velocity node at orifice• resonance• monopole ideal velocity source• monopole source amplified• dipole source at pressure anti-node

• f=100 Hz, ∆p0=12 cm H2O, divergent orifice

• Upstream and downstream volume velocity sources agree well


Orifice area function

• Resonance in both subglottal and supraglottal systems (first resonance around 450 Hz)

• This causes errors in reflection coefficient measurements and leads to the failure of the iteration method

• Area can still be predicted using measured sound pressure and statically measured orifice discharge coefficient

0 500 1000 1500 20000

10

20

30

40

50

60

10lo

g 10Z

Frequency (Hz)

SupraglottaSubglottal

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.202468

1012141618

Orif

ice

area

(mm

2 )


AreaMeasureAreaPredict

f=100 Hz, ∆p0=12 cm H2O, divergent orifice


Tonal Component Results

• Good agreement between measured upstream sound pressure and prediction from quasi-steady assumption

• Quasi-steady assumption valid for different orifice shapes at different operating conditions (driving frequency up to 120Hz)

• Suggests monopole model could be used in conjunction with 3-D incompressible steady numerical models


Broadband Sound Production by Non-stationary Turbulent Jets

Periodic component obtained by ensemble-averaging method, and extracted from signals

Statistics of turbulent sound in non-stationary flow at a particular instant compared to those for comparable stationary flow


SPEECH

Plosives Phonation Fricatives

Periodic component Broadband random component

Monopolesound

Periodic component of dipole

Random component of dipole

Quadrupolesound

Small in amplitude, neglected

weak acoustic

loadsBroadband sound

Quasi-steady Approximation Verification

Dipole

strong acoustic

loads


Broadband Sound in Pulsating JetsOrifice area is forced at specific

frequencySound pressure is decomposed into a

periodic component and a broadband component

Periodic component obtained by ensemble-average method

Broadband sound obtained by removing periodic component sound from measured pressure

Characteristics of broadband sound for non-stationary jet at a particular instant compared to those of stationary jets with same flow and orifice geometry

Two methods:• Probability density function (PDF)• Wavelet transform

Measured sound pressure

Ensemble-averaged periodic component

Turbulence generated sound


-5 0 50

0.2

0.4

0.6

0.8

t=0.

96T

Up

Sound pressure -- cmH2O

Non-sS.

-5 0 50

0.2

0.4

0.6

0.8

t=0.

96T

Dow

n


Non-sS.

-5 0 50

0.2

0.4

0.6

0.8

t=0.

51T

Up


Non-sS.

-5 0 50

0.2

0.4

0.6

0.8

t=0.

51T

Dow

n


Non-sS.

Comparison betweenprobabilitydensity functions

Broadband Sound Production by Non-stationary Turbulent Jets


0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

12

14

16

18

gf

edc

ba

Orif

ice

area

(mm

2 )


•Agreement between PDFs evolves during one cycle• Poor agreement during the

beginning of orifice opening•Agreement improves as the orifice

continues to open•Agreement decreases as the orifice

begins to close

a b c d

gfe f=20 Hz,∆p0=12 cm H2O,Divergent orifice.

-5 -4 -3 -2 -1 0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0PD

F

Acoustic pressure (Pa)-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

PDF


0.0

0.2

0.4

0.6

0.8

1.0

PDF


0.0

0.2

0.4

0.6

0.8

1.0

PDF

Acoustic pressure (Pa)

-5 -4 -3 -2 -1 0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

PDF


0.0

0.2

0.4

0.6

0.8

1.0

PDF


-5 -4 -3 -2 -1 0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

PDF



0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

12

14

16

18

a gf

ed

c

b

Orif

ice

area

(mm2 )


a b c d

gfe f=200 Hz,∆p0=12 cm H2O,Divergent orifice

-5 -4 -3 -2 -1 0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0PD

F


0.0

0.2

0.4

0.6

0.8

1.0

PDF


0.0

0.2

0.4

0.6

0.8

1.0

PDF


0.0

0.2

0.4

0.6

0.8

1.0

PDF


-5 -4 -3 -2 -1 0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

PDF


0.0

0.2

0.4

0.6

0.8

1.0

PDF


0.0

0.2

0.4

0.6

0.8

1.0

PDF


•As driving frequency increases, general agreement between PDFsdecreases, especially during the orifice opening stage• quasi-steady approximation may not

be valid for broadband component


Wavelet AnalysisProvides time information as well as frequency informationIn STFT the size of the sliding window is fixed, while in

wavelet analysis the window size is changeable, therefore giving same resolution for different frequency component

Daubechies 1 wavelet (a step function) used (similar results obtained with db2)

7-level wavelet transform used in this studySignal

A1 D1

A2 D2

D7A7D: DetailA: Approximation

S=A7+D7+D6+D5+D4+D3+D2+D1

At each level, signal is decomposed into a Detail and an Approximation. The Detail corresponds to the high frequency component while the Approximationcorresponds to the low frequency component.


Wavelet Coefficients

0 1 2 3 40.00.51.0

t

j

07

14

i

0.080.12

h

0.080.12

g

0.040.080.12

f

0.10.2

e

0.20.30.4

d

0.20.40.6

c

0.30.6

b

0.40.81.2

a

Straight,20 Hz,12 cmH2O

Divergent,200 Hz,12 cmH2O

Convergent,200 Hz,12 cmH2O

0 1 2 3 40.40.60.8

t

j

51015

i

0.150.200.25

h

0.10.20.3

g

0.20.4

f

0.20.30.4

e

0.20.4

d

0.30.6

c

0.30.60.9

b

0.40.5

a

-2 0 2

60000120000180000

t

i

0.060.09

h

0.05

0.10

g

0.050.100.15

f

0.00.10.2

e

0.00.10.2

d

0.00.10.2

c

0.10.20.3

b

0.20.4

a

0

188

368

764

1504

3072

6184

14576

Hz

A

U6A2


Summary• Turbulent sound synchronous with

modulation of orifice area• Two peaks during one cycle:• first peak may be associated with the

developing of the jet• second peak associated with the quenching of

the flow during closure.• First peak less apparent for high-frequency

component• For same level of details, first peak becomes

less apparent as the driving frequency increases


• quasi-steady approximation verified in confined jets for tonal sound component across various flow conditions, orifice geometries, and acoustic loads

• non-stationary broadband investigated using PDF comparisons and wavelet analysis

• broadband sound generation appears to be non-stationary (not quasi-steady)

Conclusions


Ongoing Work

Validation of quasi-steady assumption• Coanda Effect• Complex geometries (pathological)

Acoustic scaling laws• Tonal and broadband• Evaluate impact on articulatory speech

synthesisAdina Simulations


For more …

Zhaoyan Zhang, “Experimental study of sound generation by confined jets with application to human phonation,” Ph.D. Dissertation, Purdue University, 2002.Cheng Zhang, “____,” M.S.M.E. Thesis, Purdue University, 2002.Wei Zhao, “A numerical investigation of sound generated from subsonic jets with application to human phonation,” Ph.D. Thesis, Purdue University, 2000.

verification of the quasi-steady approximation for sound ... · approximation for sound generation...

Documents